Pseudospin symmetry for a noncentral electric dipole ring-shaped potential in the tridiagonal representation

Abstract

A noncentral harmonic oscillatory ring-shaped potential is proposed, in which the noncentral electric dipole is included. The pseudospin symmetry for this potential is investigated by working in a complete square integrable basis that supports a tridiagonal matrix representation of the wave operator. The resulting three-term recursion relations for the expansion coefficients of the wavefunctions (both angular and radial) are presented. The angular/radial wavefunction is written in terms of the Jacobi/Laguerre polynomials. The discrete spectrum of the bound state is obtained by diagonalizing the radial recursion relation. The algebraic property of energy equation is also discussed, showing the exact pseudospin symmetry